Said Jabbour

Control-based clause sharing in parallel SAT solving

Conflict driven clause learning, one of the most important component of modern SAT solvers, is also recognized as very important in parallel SAT solving. Indeed, it allows clause sharing between multiple processing units working on related (sub) problems. However, without limitation, sharing clauses might lead to an exponential blow up in communication or to the sharing of irrelevant clauses. This paper, proposes two innovative policies to dynamically adjust the size of shared clauses between any pair of processing units. The first approach controls the overall number of exchanged clauses whereas the second additionally exploits the relevance quality of shared clauses. Experimental results show important improvements of the state-of the-art parallel SAT solver.

A generalized framework for conflict analysis

This paper presents an extension of Conflict Driven Clauses Learning (CDCL). It relies on an extended notion of implication graph containing additional arcs, called inverse arcs. These are obtained by taking into account the satisfied clauses of the formula, which are usually ignored by conflict analysis. This extension captures more conveniently the whole propagation process, and opens new perspectives for CDCL-based approaches. Among other benefits, our extension leads to a new conflict analysis scheme that exploits the additional arcs to back-jump to higher levels. Experimental results show that the integration of our generalized conflict analysis scheme within two state-of-the-art solvers improves their performance.

Diversification and intensification in parallel SAT solving

In this paper, we explore the two well-known principles of diversification and intensification in portfolio-based parallel SAT solving. These dual concepts play an important role in several search algorithms including local search, and appear to be a key point in modern parallel SAT solvers. To study their trade-off, we define two roles for the computational units. Some of them classified as Masters perform an original search strategy, ensuring diversification. The remaining units, classified as Slaves are there to intensify their masters strategy. Several important questions have to be answered. The first one is what information should be given to a slave in order to intensify a given search effort? The second one is, how often, a subordinated unit has to receive such information? Finally, the question of finding the number of subordinated units and their connections with the search efforts has to be answered. Our results lead to an original intensification strategy which outperforms the best parallel SAT solver ManySAT, and solves some open SAT instances.

A SAT-based approach for discovering frequent, closed and maximal patterns in a sequence

In this paper we propose a satisfiability-based approach for enumerating all frequent, closed and maximal patterns with wildcards in a given sequence. In this context, since frequency is the most used criterion, we introduce a new polynomial inductive formulation of the cardinality constraint as a Boolean formula. A nogood-based formulation of the anti-monotonicity property is proposed and dynamically used for pruning. This declarative framework allows us to exploit the efficiency of modern SAT solvers and particularly their clause learning component. The experimental evaluation on real world data shows the feasibility of our proposed approach in practice.

The Top- k frequent closed itemset mining using Top- k SAT problem

In this paper, we introduce a new problem, called Top-k SAT, that consists in enumerating the Top-k models of a propositional formula. A Top-k model is defined as a model with less than k models preferred to it with respect to a preference relation. We show that Top-k SAT generalizes two well-known problems: the partial Max-SAT problem and the problem of computing minimal models. Moreover, we propose a general algorithm for Top-k SAT. Then, we give the first application of our declarative framework in data mining, namely, the problem of enumerating the Top-k frequent closed itemsets of length at least min (FCIMkmin). Finally, to show the nice declarative aspects of our framework, we encode several other variants of FCIMkmin into the Top-k SAT problem.

Measuring inconsistency through minimal proofs

Measuring the degree of inconsistency of a knowledge base provides important context information for making easier inconsistency handling. In this paper, we propose a new fine-grained measure to quantify the degree of inconsistency of propositional formulae. Our inconsistency measure uses in an original way the minimal proofs to characterize the responsibility of each formula in the global inconsistency. We give an extension of such measure to quantify the inconsistency of the whole base. Furthermore, we show that our measure satisfies the important properties characterizing an intuitive inconsistency measure. Finally, we address the problem of restoring consistency using an inconsistency measure.

Boolean satisfiability for sequence mining

In this paper, we propose a SAT-based encoding for the problem of discovering frequent, closed and maximal patterns in a sequence of items and a sequence of itemsets. Our encoding can be seen as an improvement of the approach proposed in [8] for the sequences of items. In this case, we show experimentally on real world data that our encoding is significantly better. Then we introduce a new extension of the problem to enumerate patterns in a sequence of itemsets. Thanks to the flexibility and to the declarative aspects of our SAT-based approach, an encoding for the sequences of itemsets is obtained by a very slight modification of that for the sequences of items.

Enumerating Prime Implicants of Propositional Formulae in Conjunctive Normal Form

In this paper, a new approach for enumerating the set prime implicants (PI) of a Boolean formula in conjunctive normal form (CNF) is proposed. It is based on an encoding of the input formula as a new one whose models correspond to the set of prime implicants of the original theory. This first PI enumeration approach is then enhanced by an original use of the boolean functions or gates usually involved in many CNF instances encoding real-world problems. Experimental evaluation on several classes of CNF instances shows the feasibility of our proposed framework.

Decomposition Based SAT Encodings for Itemset Mining Problems

Recently, several constraint programming (CP)/propositional satisfiability (SAT) based encodings have been proposed to deal with various data mining problems including itemset and sequence mining problems. This research issue allows to model data mining problems in a declarative way, while exploiting efficient and generic solving techniques. In practice, for large datasets, they usually lead to constraints network/Boolean formulas of huge size. Space complexity is clearly identified as the main bottleneck behind the competitiveness of these new declarative and flexible models w.r.t. specialized data mining approaches. In this paper, we address this issue by considering SAT based encodings of itemset mining problems. By partitioning the transaction database, we propose a new encoding framework for SAT based itemset mining problems. Experimental results on several known datasets show significant improvements, up to several orders of magnitude.

Prime implicates based inconsistency characterization

Measuring inconsistency is recognized as an important issue for handling inconsistencies [5, 6]. Based on prime implicates canonical representation, we first characterize the conflicting variables allowing us to refine an existing inconsistency measure. Secondly, we propose a new measure, to circumscribe the internal conflicts in a knowledge base. This measure is proved to satisfy a new but weaker form of dominance.